Geodesic
Almost periodic sequences and functions with given values
Archivum mathematicum, Tome 47 (2011) no. 1, pp. 1-16 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set $X$ in a metric space, it is proved the existence of an almost periodic sequence $\lbrace \psi _k\rbrace _{k \in \mathbb{Z}}$ such that $\lbrace \psi _k; \, k \in \mathbb{Z}\rbrace = X$ and $\psi _k = \psi _{k + l q(k)}$, $l \in \mathbb{Z}$ for all $k$ and some $q(k) \in \mathbb{N}$ which depends on $k$.
We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set $X$ in a metric space, it is proved the existence of an almost periodic sequence $\lbrace \psi _k\rbrace _{k \in \mathbb{Z}}$ such that $\lbrace \psi _k; \, k \in \mathbb{Z}\rbrace = X$ and $\psi _k = \psi _{k + l q(k)}$, $l \in \mathbb{Z}$ for all $k$ and some $q(k) \in \mathbb{N}$ which depends on $k$.
Classification : 11K70, 42A75
Keywords: almost periodic functions; almost periodic sequences; almost periodicity in metric spaces 
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     title = {Almost periodic sequences and functions  with given values},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2011_47_1_a0/}
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Veselý, Michal. Almost periodic sequences and functions  with given values. Archivum mathematicum, Tome 47 (2011) no. 1, pp. 1-16. http://geodesic.mathdoc.fr/item/ARM_2011_47_1_a0/

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